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Two infinite planes each with uniform su...

Two infinite planes each with uniform surfao charge density `+sigma C/m^(2)` are kept in such a wa m that the angle between them is 30°. Th electric field in the region shown between then is given by:

A

`sigma/(2epsilon_(0))[(1+sqrt(3)/2)haty - 1/2hatx]`

B

`sigma/(2epsilon_(0))[(1-sqrt(3)/2)haty -1/2hatx]`

C

`sigma/(2epsilon_(0))[(1-sqrt(3)/2]haty + 1/2hatx]`

D

`sigma/(2epsilon_(0))[(1+sqrt(3)/2)haty + 1/2hatx]`

Text Solution

Verified by Experts

The correct Answer is:
B

`vecE_(1) = sigma/(2epsilon_(0))(hatj)`
`vecE_(2) = sigma/(2epsilon_(0)) sin60^(@) (-hatj) + sigma/(2epsilon_(0))cos60^(@)(-hati)`
`=sigma/(2epsilon_(0)) xx sqrt(3)/2hatj -sigma/(2epsilon_(0)) xx 1/2hati`
`therefore` Resultant electric field,
`vecE =vecE_(1) + vecE_(2)`
`=sigma/(2epsilon_(0))hatj - sigma/(2epsilon_(0)) xx sqrt(3)/2hatj - sigma/(2epsilon_(0)) xx 1/2hati`
`=sigma/(2epsilon_(0))[(1-sqrt(3)/2)haty - 1/2hatx]`
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